test-skybox/CatalogSkybox.js

const CatalogSkybox = {

};

/**
 * 由立方体盒子上的坐标(单位长度为2)转换为对应盒子面上的图片的坐标
 * 
 * @param {number} x 立方盒子的x坐标,[-1,1] 
 * @param {number} y 立方盒子的y坐标,[-1,1]
 * @param {number} z 立方盒子的z坐标,[-1,1] 
 * @returns {i,j,faceId} i为图片的x坐标(向右),[0,1],j为图片的y坐标(向下),[0,0]为图片的左上角
 * faceId为图片的面id,[0,5]
 */
CatalogSkybox.cubeXyzToImgUV = function(x, y, z) {
    let faceId, i, j;

    if (x === -1) { // back
        j = (1.0 - y) / 2.0;
        i = (1.0 + z) / 2.0;
        faceId = 0;
    } else if (y === -1) { // left
        i = (1.0 + x) / 2.0;
        j = (1.0 - z) / 2.0;
        faceId = 1;
    } else if (x === 1) { // front
        j = (1.0 - y) / 2.0;
        i = (1.0 - z) / 2.0;
        faceId = 2;
    } else if (y === 1) { // right
        i = (1.0 + x) / 2.0;
        j = (1.0 + z) / 2.0;
        faceId = 3;
    } else if (z === 1) { // top
        i = (1.0 + x) / 2.0;
        j = (1.0 - y) / 2.0;
        faceId = 4;
    } else if (z === -1) { // bottom
        i = (1.0 - x) / 2.0;
        j = (1.0 - y) / 2.0;
        faceId = 5;
    }
    else {
        throw new Error("x,y,z其中一个必须为1或-1");
    }

    if (i > 1) {
        i = 1;
    }
    if (i < 0) {
        i = 0;
    }
    if (j > 1) {
        j = 1;
    }
    if (j < 0) {
        j = 0;
    }

    return { i, j, faceId };
}

const Pi1_4 = Math.PI / 4.0;
const Pi3_4 = 3 * Math.PI / 4.0;
/**
 * 天球坐标系坐标(赤经,赤纬)转换为立方体盒子(单位为2）上的坐标
 * 
 * @param {number} theta 赤经,弧度,[-PI,PI] 
 * @param {number} phi 赤纬,弧度,[-PI/2,PI/2] 
 */
CatalogSkybox.sphere2CubeXyz = function (theta, phi) {

    // 计算笛卡尔坐标（单位长度为1的球表面）
    let x = Math.cos(theta) * Math.cos(phi);
    let y = Math.sin(theta) * Math.cos(phi);
    let z = Math.sin(phi);

    const tanPhi = Math.tan(phi);
    let cosThe;
    // 将笛卡尔坐标映射到立方体盒子(单位为2)上

    //  x = 1,或 z = 1,-1
    if (theta >= -Pi1_4 && theta < Pi1_4) {
        cosThe = Math.cos(theta);
        if (tanPhi > cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = 1;
        }
        else if (tanPhi < -cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = -1;
        }
        else {
            y = y / Math.abs(x);
            z = z / Math.abs(x);
            x = 1;
        }
    }
    // y = 1,或 z = 1,-1
    else if (theta >= Pi1_4 && theta < Pi3_4) {
        cosThe = Math.cos(theta - Math.PI / 2);
        if (tanPhi > cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = 1;
        }
        else if (tanPhi < -cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = -1;
        }
        else {
            x = x / Math.abs(y);
            z = z / Math.abs(y);
            y = 1;
        }
    }
    //  x = -1,或 z = 1,-1
    else if (theta >= Pi3_4 || theta < -Pi3_4) {
        cosThe = Math.cos(theta - Math.PI);
        if (tanPhi > cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = 1;
        }
        else if (tanPhi < -cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = -1;
        }
        else {
            y = y / Math.abs(x);
            z = z / Math.abs(x);
            x = -1;
        }
    }
    //  y = -1,或 z = 1,-1
    else if (theta >= -Pi3_4 && theta < -Pi1_4) {
        cosThe = Math.cos(theta + Math.PI / 2);
        if (tanPhi > cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = 1;
        }
        else if (tanPhi < -cosThe) {
            x = x / Math.abs(z);
            y = y / Math.abs(z);
            z = -1;
        }
        else {
            x = x / Math.abs(y);
            z = z / Math.abs(y);
            y = -1;
        }
    }
    return { x, y, z };
}

/**
 * 由立方体盒子某个面的图片坐标转换为对应立方盒子面的坐标
 * 
 * @param {number} i 图片的x坐标(向右),[0,1]  
 * @param {number} j 图片的y坐标(向下),[0,0]为图片的左上角 
 * @param {number} faceId 立方盒子的面id,[0,5] 
 * @returns {x,y,z} 立方盒子的坐标,[-1,1]
 */
CatalogSkybox.imgUvToCubeXyz = function(i, j, faceId) {
    /*
     * 此函数被修改以适应cesium skybox的贴图
     */
    let a = 2.0 * i ;
    let b = 2.0 * j;

    let x, y, z;
    if (faceId === 0) { // back
        // (x,y,z) = (-1.0, 1.0 - a, 1.0 - b);
        x = -1.0;
        y = 1.0 - b;
        z = a - 1.0;
    } else if (faceId === 1) { // left
        x = a - 1.0;
        y = -1.0;
        z = 1.0 - b;
    } else if (faceId === 2) { // front
        // (x,y,z) = (1.0, a - 1.0, 1.0 - b);
        x = 1.0;
        y = 1.0 - b;
        z = 1.0 - a;
    } else if (faceId === 3) { // right
        // (x,y,z) = (1.0 - a, 1.0, 1.0 - b);
        x = a - 1.0;
        y = 1.0;
        z = b - 1.0;
    } else if (faceId === 4) { // top
        // (x,y,z) = (b - 1.0, a - 1.0, 1.0);
        x = a - 1.0;
        y = 1.0 - b;
        z = 1.0;
    } else if (faceId === 5) { // bottom
        // (x,y,z) = (1.0 - b, a - 1.0, -1.0);
        x = 1.0 - a;
        y = 1.0 - b;
        z = -1.0;
    }

    return { x, y, z };
}


/**
 * 由立方体盒子上的坐标(单位长度为2)转换为赤经赤纬坐标
 * 
 * @param {number} x 立方盒子的x坐标,[-1,1]
 * @param {number} y 立方盒子的y坐标,[-1,1]
 * @param {number} z 立方盒子的z坐标,[-1,1]
 * @returns {theta, phi} theta为赤经,弧度,[-PI,PI],phi为赤纬,弧度,[-PI/2,PI/2]
 */
CatalogSkybox.cubeXyz2Sphere = function (x, y, z) {
    let theta = Math.atan2(y, x);
    let r = Math.sqrt(x * x + y * y);
    let phi = Math.atan2(z, r);
    return { theta, phi };
}


export default CatalogSkybox;